Geomery Question: The area of a hexagon with sides 3 ft on each side.?

Question

Barney wants to use felt to cover the top of a regular-hexagonal game table. Each side is 3 feet long.
A. what is the area to be covered?
B. Felt comes 72 inches wide. Can barney cover the table top without having a seam in the felt?

I would appeciate all help and if you solve it can you please explain how you solved it.

Answer 1

You can divide a hexagon into six identical triangles, each with three equal sides. Draw this out on a piece of paper.

Now draw a line from the centre to the middle of the opposite side of one of the triangles. This is the height of the triangle. The height of an equilateral triangle is sqrt(3)/2 times the base. (standard result)

You should now be able to work out the area of one of the triangles. THen multiply by six to get the area of the hexagon.

THe height (or width if you like) of the hexagon is related to the height of the triangle very simply. Can you see it?

You should be able to

Answer 2

This hexagon can be cut up into 6 equal triangles all with 3 foot sides. 1 triangle can be cut in half where the base is 1.5 ft and the hypotenuse is 3 ft. So the height is sqrt(3^2 - 1.5^2), which is 2.598 ft. The area is 1/2 X 2.598 X 1.5 = 1.95 sq ft. there are 12 of these triangles so the total area is 23.4 sq ft. Since the distance from the center of the table to the center of 1edge is 2.598 ft, the distance across is 5.196 ft. which is 62.352 inches so the felt won't need a seam.

Answer 3

The hexagon is made up of 6 equilateral triangles.The area of an equilateral triangle is (s^2/4)sqrt(3) = (3^2/4)sqrt(3).
So area of hexagon = (6)(9/4)(sqrt(3) approx = 23.38 ft^2.

72 inches = 6 feet so if he buys a 6 foot length he will have 6*6 = 36 ft^2 which is more than enough to cover the table.

Answer 4

a hexagon can be made up of 6 equilateral triangles, each with side 3ft

the area of one triangle is 1/2 x base x height
height can be worked out using pythagoras' theorem
height^2 = 3^2 - 1.5^2
height = 2.60 ft
area = 1/2 x 3 x 2.60
area = 3.90 ft^2

So the area fo the total hexagon
6 x 3.90 = 23.4 ft^2

The maximum distance that needs to be covered on the table is a diameter, which can be seen (when the hexagon is split into the triangles) to be
2 x side length
= 6ft
= 72 inches

so he can cover it (but not have it draping over the edge etc)

Answer 5

section= a million/2 a p a is the apothum p is the fringe the fringe is common...12(6)=seventy two For the apothum, bear in mind your 30 60 ninety triangle... the quick leg is 6, so the long leg is 6rad3 A = a million/2 (6rad3)(seventy two) = 216rad3. so in spite of 216 situations the squreroot of three is...i've got not got a calculator.

Answer 6

It's GEOMETRY. LEARN TO SPELL

Answer 7

(I'm a teacher...) 23.38 feet squared.... but how?